A truncated theta identity of Gauss and overpartitions into odd parts

DOI10.1007/s00026-019-00442-xzbMath1448.11181OpenAlexW4235997424WikidataQ127093095 ScholiaQ127093095MaRDI QIDQ2299107

Mircea Merca, Ae Ja Yee, Chun Wang

Publication date: 20 February 2020

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00026-019-00442-x

zbMATH Keywords

theta seriesoverpartitionsrecurrences

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (16)

Infinite families of Hecke-Rogers type series and their truncated representations ⋮ Truncated versions of three identities of Euler and Gauss ⋮ On the Ramanujan-type congruences modulo 8 for the overpartitions into odd parts ⋮ Linear inequalities concerning partitions into distinct parts ⋮ A further look at cubic partitions ⋮ Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series ⋮ Linear inequalities concerning the sum of the distinct parts congruent to r modulo m in all the partitions of n ⋮ 4-regular partitions and the pod function ⋮ 6-regular partitions: new combinatorial properties, congruences, and linear inequalities ⋮ Rank partition functions and truncated theta identities ⋮ Unnamed Item ⋮ ON THE SUM OF PARTS IN THE PARTITIONS OF n INTO DISTINCT PARTS ⋮ On a nonlinear relation for computing the overpartition function ⋮ New truncated theorems for three classical theta function identities ⋮ Generalizations of Stanley's theorem: combinatorial proofs and related inequalities ⋮ A reversal of Schur's partition theorem

Cites Work

• Unnamed Item
• Unnamed Item
• The truncated pentagonal number theorem
• A truncated Jacobi triple product theorem
• Proofs of two conjectures on truncated series
• Interpreting the truncated pentagonal number theorem using partition pairs
• Bilateral truncated Jacobi's identity
• Some new expansions for certain truncated \(q\)-series
• Truncated series from the quintuple product identity
• Arithmetic properties of overpartitions into odd parts
• Combinatorial proofs of two truncated theta series theorems
• Truncated theta series and a problem of Guo and Zeng
• \(q\)-Pell sequences and two identities of V. A. Lebesgue
• On pairs of partitions with steadily decreasing parts
• Two truncated identities of Gauss
• Truncated Jacobi triple product series
• Some Hecke-Rogers type identities
• On the number of overpartitions into odd parts
• A combinatorial proof of the Rogers--Ramanujan and Schur identities
• Another approach to the Truncated Pentagonal Number Theorem
• Overpartitions
• A further look at the truncated pentagonal number theorem

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